To find the slope of the line passing through the points (2, -6) and (6, -12), we can use the slope formula. The slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let's identify the given points:
- The first point is [tex]\((x_1, y_1) = (2, -6)\)[/tex]
- The second point is [tex]\((x_2, y_2) = (6, -12)\)[/tex]
We can now substitute these coordinates into the slope formula.
First, calculate the difference in the y-coordinates:
[tex]\[ y_2 - y_1 = -12 - (-6) \][/tex]
[tex]\[ y_2 - y_1 = -12 + 6 \][/tex]
[tex]\[ y_2 - y_1 = -6 \][/tex]
Next, calculate the difference in the x-coordinates:
[tex]\[ x_2 - x_1 = 6 - 2 \][/tex]
[tex]\[ x_2 - x_1 = 4 \][/tex]
Now, we can find the slope by dividing these differences:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
[tex]\[ m = \frac{-6}{4} \][/tex]
[tex]\[ m = -1.5 \][/tex]
So, the slope of the line that passes through the points (2, -6) and (6, -12) is [tex]\(-1.5\)[/tex].
